After I press that button, spine turns into small window and opens Open project menu. After that I have no more ability to interact with it. Spine stops responding. It's not possible to switch to spine window anymore. The same happens when I try to save project.

Neither error messages nor CTDs.

Here's a window sample and a log file. It happend today, after update.

If you need extra information - I've no problem with it. You can ask whatever you need.

Note: Trial version works fine.
Note: Spine is not shown on "Programs and Features" list. Trial version is ok with this.
Note: Spine's app icon is not shown

UPD: I've fixed that by removing all spine data in system directories and reinstalling Spine to a different folder.

No. A wasn't able to do that.